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Veseljchak [2.6K]
3 years ago
7

A real estate company owns 120 apartments which are fully occupied when the rent is $650 per month. Analytics indicate that for

each $25 increase in rent, 4 apartments will become unoccupied. What rent should be charged in order to obtain the largest gross income

Business
2 answers:
chubhunter [2.5K]3 years ago
6 0

Answer:

The rent that should be charged to maximize gross icome is $700.

Explanation:

The rent can be increased by $25 steps.

The rent equation can be written as,

Rent = 650 + 25x

The Apartments occupied will fall by 4 apartments everytime the rent is increased by $25.

The apartment occupancy equation can be written as,

Apparment occuoancy = 120 - 4x

Where, x is the number of times the rent is increased by $25.

The revenue will be,

Revenue = Rent * No of apartments occupied

Revenue = (650 + 25x) * (120 - 4x)

Solving the equation we get quadratic equation,

Revenue = 78000 - 2600x + 3000x - 100x²

0 = 78000 + 400x - 100x²

As we need the change, we need to take the derivative of this equation.

d/dx = 0 + 1 * 400x° - 2 * 100x

400 - 200x = 0

400 = 200x

400 / 200 = x

x = 2

Thus, the rent that should be charged to amximize gross income is,

Rent = 650 + 25 * (2)  = $700 per apartment

The revenue at this rent will be,

Revenue = 700 * [120 - 4 * (2)] = $78400

Free_Kalibri [48]3 years ago
6 0

Answer:

Check the explanation

Explanation:

This is a question under Calculus <em><u>(which is another segment of mathematics and it is utilized for understanding the changes between values that are related by a function.  Calculus is used in a lot of diverse fields of study such as astronomy, physics, biology, economics, medicine, engineering and sociology).</u></em>

The step by step solution to the above question can be seen in the attached image below:

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